It takes 0 (not 2) bananas to go 0 miles into the desert. It takes 1 banana (not 2) to go 1 mile into the desert. It takes 2 bananas to go 2 miles into the desert. I suspect it takes 6 (not 3 nor 7) bananas to go 3 miles into the desert, but don't ask me how to accomplish it...

Which means we may not know exactly how many bananas it takes to reach the next milestone. It is approximately 326 but, in my 20-second perusal of the links provided, I don't see an exact answer.

Update: You can get 3 miles on 6 bananas:

At
  0: eat 1, carry 1 (2 used)
1/2: drop 1 (1/2 in stomach, 1@1/2)
  0: eat 1, carry 1 (4 used)
1/2: drop 1 (1/2 in stomach, 2@1/2)
  0: eat 1, carry 1 (6 used)
3/4: drop 1 (1/4 in stomach, 2@1/2, 1@3/4)
1/2: eat 1, carry 1 (0@1/2, 1@3/4)
  1: drop 1 (1/2 in stomach, 1@3/4, 1@1)
3/4: carry 1 (1/4 in stomach, 0@3/4, 1@1)
  1: eat 1 (0@1, still carrying 1)
  2: eat 1 (carrying 0)
  3: hope the report of "bananas 3 miles in" are true
[download]

Update2: And you can get 4 miles w/ 22 bananas:

At
  0: eat 1, carry 1 (2 used)
1/2: drop 1 (1/2 in stomach, 1@1/2)
  0: repeat above 9 more times (20 used, 10@1/2)
  0: eat 1, carry 1 (22 used)
3/4: drop 1 (1/4 in stomach, 10@1/2, 1@3/4)
1/2: eat 1, carry 1 (8@1/2, 1@3/4)
  1: drop 1 (1/2 in stomach, 8@1/2, 1@3/4, 1@1)
1/2: repeat above 3 times (2@1/2, 1@3/4, 4@1)
1/2: eat 1, carry 1 (0@1/2, 1@3/4, 4@1)
  1: drop 1 (1/2 in stomach, 1@3/4, 5@1)
3/4: carry 1 (1/4 in stomach, 0@3/4, 5@1)
  1: drop 1 (stomach empty, 6@1)
  1: move 3 miles futher in using previous answer
[download]